Solving a cryptarithm

# /. Solve[{   10^2 d + 10 e + f + 10^2 f + 10 e + f == 10^2 g + 10 h + h,
            2 (10^2 k + 10 l + m) == 10^2 n + 10 k + l,
            3 (10^2 a + 10 b + c) == 10^2 b + 10 b + b} ~ Join ~
          Thread[0 <= # <= 9 &@#], #, Integers]& @ {a, b, c, d, e, f, g, h, k, l, m, n} 
    // Short[#, 6] &

 {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 2},
 {0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 3, 5},
 {0, 0, 0, 0, 0, 0, 0, 0, 3, 6, 8, 7},
 {0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 1, 8},
 {0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0},
  <<739>>, 
 {1, 4, 8, 9, 0, 0, 9, 0, 0, 0, 0, 0},
 {1, 4, 8, 9, 0, 0, 9, 0, 1, 0, 5, 2},
 {1, 4, 8, 9, 0, 0, 9, 0, 2, 6, 3, 5},
 {1, 4, 8, 9, 0, 0, 9, 0, 3, 6, 8, 7},
 {1, 4, 8, 9, 0, 0, 9, 0, 4, 2, 1, 8}}

It yields the result instantanously. Mind Slot ( #) appears here in the three contexts, thus we had to put the symbol & in appropriate places where the pure functions end.

v = {100, 10, 1};

{#, Variables[List @@ #]} & /@
 {
  v.{d, e, f} + v.{f, e, f} == v.{g, h, h},
  2*v.{k, l, m} == v.{n, k, l},
  3*v.{a, b, c} == v.{b, b, b}
 }

FindInstance[Join[{#}, Thread[10 > #2 > 0]], #2, Integers] & @@@ %

{{{d -> 3, e -> 3, f -> 3, g -> 6, h -> 6}},
 {{k -> 2, l -> 6, m -> 3, n -> 5}},
 {{a -> 1, b -> 4, c -> 8}}}